Quasi-optimal and robust a posteriori error estimates in $L^{\infty}(L^{2})$ for the approximation of Allen-Cahn equations past singularities
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Publication:3168722
DOI10.1090/S0025-5718-2010-02444-5zbMath1215.65149MaRDI QIDQ3168722
Publication date: 19 April 2011
Published in: Mathematics of Computation (Search for Journal in Brave)
mean curvature flowfinite element methodnumerical experimentsadaptive methodsa posteriori error estimatesGalerkin methodsAllen-Cahn equationelliptic reconstruction
Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)
Related Items (15)
Robust a posteriori estimates for the stochastic Cahn-Hilliard equation ⋮ Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems ⋮ Error estimates with low-order polynomial dependence for the fully-discrete finite element invariant energy quadratization scheme of the Allen–Cahn equation ⋮ Analysis and approximations of an optimal control problem for the Allen-Cahn equation ⋮ Mean curvature flow by the Allen–Cahn equation ⋮ Recovery type a posteriori error estimation of an adaptive finite element method for Cahn-Hilliard equation ⋮ Error control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential ⋮ Some algorithms for the mean curvature flow under topological changes ⋮ Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations ⋮ Recovery type a posteriori error estimation of adaptive finite element method for Allen-Cahn equation ⋮ A Posteriori Error Estimates for the Allen--Cahn Problem ⋮ Stability analysis and best approximation error estimates of discontinuous time-stepping schemes for the Allen–Cahn equation ⋮ A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems ⋮ Delay-dependent elliptic reconstruction and optimal 𝐿^{∞}(𝐿²) a posteriori error estimates for fully discrete delay parabolic problems ⋮ On a posteriori error control for the Allen-Cahn problem
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